Exact Localization of Acoustic Reflectors from Quadratic Constraints

In this paper we discuss a method for localizing acoustic reflectors in space based on acoustic measurements on source-to-microphone reflective paths. The method converts Time of Arrival (TOA) and Time Difference of Arrival (TDOA) into quadratic constraints on the line corresponding to the reflector. In order to be robust against measurement errors we derive an exact solution for the minimization of a cost function that combines an arbitrary number of quadratic constraints. Moreover we propose a new method for the analytic prediction of reflector localization accuracy. This method is sufficiently general to be applicable to a wide range of estimation problems.